Twice the distance to the plane of the mirror. Don't forget that you need to move the camera away from your face, perhaps a tripod or similar. Don't use flash directly into the mirror (90 degrees), offset your camera and image slightly.
Focussing works the same way as focussing for the eye, which is to detect highest energy levels. This would not be on the mirror plane but on the object plane.
I think it would surely fool a camera autofocus system, but I guess it depends on how the system works. A radar type device would report the distance to the solid plane of the mirror, but maybe some parallax system would measure distance to the image, any camera techies know for sure ??
think it's energies no? You can run a fourier transform on the spatial frequencies of different focal ranges, until you find the one with the highest energy content through contrasts.
Asit happens I took some pictures of subjects in a mirror at the weekend and the autofocus on my Olympus C750 worked perfectly which it doesn't always!
Can u do it again please and tell us what happens? Can you selotape some card to the top of the mirror, focus on an object in the mirror, and see if the settings change when you focus on the card. cheers.